Sentaurus Process
9. Special Focus: Meshing

9.1 Overview
9.2 Initialization
9.3 Remeshing
9.4 Refinement Boxes

Objectives

• To demonstrate the most important remeshing options available in Sentaurus Process.

9.1 Overview

The files discussed in this section are part of the Sentaurus Workbench project Remeshing. The complete project can be investigated from within Sentaurus Workbench in the directory Applications_Library/GettingStarted/sprocess/Remeshing.

Two mesh generation engines are available from Sentaurus Process:

• Sentaurus Mesh
• MGOALS library, which also performs boundary movement

Since the mesh quality and reliability of Sentaurus Mesh is superior to that of MGOALS, especially in three dimensions, Sentaurus Mesh is the default meshing engine.

The generated mesh is anisotropic. The dimensions in the normal and lateral directions are set with the keywords min.normal.size, normal.growth.ratio, and max.lateral.size.

To show how to work with Sentaurus Process meshing capabilities, a simple structure is remeshed with various meshing options.

9.2 Initialization

The initial (line) mesh and a simple structure are defined:

line x location= -0.15 spacing=0.01  tag=GateTop    
line x location= -0.02 spacing=0.005                 
line x location= -0.01 spacing=0.005 tag=OxTop      
line x location=  0.0  spacing=0.005 tag=SiTop      
line x location=  0.05 spacing=0.01                  
line x location=  0.5  spacing=0.05                 
line x location=  1.0  spacing=0.2   tag=SiBottom   
                         
line y location= 0.0   spacing=0.05  tag=Mid        
line y location= 0.1   spacing=0.05  tag=Gate       
line y location= 0.4   spacing=0.05  tag=Right      
    
region Silicon     xlo=SiTop   xhi=SiBottom ylo=Mid yhi=Right
region Oxide       xlo=OxTop   xhi=SiTop    ylo=Mid yhi=Right
region PolySilicon xlo=GateTop xhi=OxTop    ylo=Mid yhi=Gate

init concentration=1.00e+15 field=Phosphorus

struct tdr=grid_mg0

See Section 3.2 Defining Initial 2D Grid and Section 3.3 Defining Simulation Domain and Initialization for details.

Figure 1. Initial line mesh.

9.3 Remeshing

After creating the initial tensor mesh, the mesh can be refined with:

mgoals min.normal.size=0.01 normal.growth.ratio=2.0
grid   remesh

The normal mesh spacing at the interface is set with the keyword min.normal.size. Away from the interface, the mesh expands and the expansion rate is set with the keyword normal.growth.ratio.

Figure 2. Remeshing with normal mesh spacing (0.01).

To highlight the effect of the normal mesh spacing, the resulting mesh for a five-times finer normal mesh spacing is shown:

mgoals min.normal.size=0.002 normal.growth.ratio=2.0
grid   remesh

Figure 3. Remeshing for five-times finer normal mesh spacing (0.002).

To highlight the effect of the expansion rate, the resulting mesh for a lower expansion rate is given:

mgoals min.normal.size=0.002 normal.growth.ratio=1.2
grid   remesh

Figure 4. Remeshing with lower expansion rate of mesh.

The effects of the various settings are clearly observed in the following animation (see Figure 5).

Figure 5. Animated snapshots of different meshing and remeshing steps.

9.4 Refinement Boxes

In process simulations, a good resolution at interfaces is important and certain regions in the bulk must be refined properly, for example, to adequately resolve a steep doping profile.

This can be accomplished with refinement boxes:

refinebox min= {-0.1 0.05} max= {0.1 0.15} xrefine= {0.015} \
  yrefine= {0.015} all add
grid remesh

The extent of the refinement box is defined with the keywords min and max. (In the Sentaurus Process coordinate system, the x-coordinate axis points downwards and the y-coordinate points to the right.)

The keywords xrefine and yrefine control the mesh spacing. If only one number is given, the mesh spacing is constant throughout the box. The keyword all activates the box for all materials, and the keyword add ensures that previously defined boxes are maintained.

Figure 6. Refinement box used for better resolution at interfaces.

In the following example, the refinement box is activated in silicon only, and the mesh in the y-direction is nonuniform. The spacing at the left side of the box is 5 nm; in the center, it is 15 nm; and at the right side, it is 2.5 nm.

refinebox min= {-0.1 -0.2} max= {0.1 -0.05} xrefine= {0.015} \
  yrefine= {0.005 0.015 0.0025} Silicon add
grid remesh

Figure 7. Activation of refinement box in silicon.

The effects of the various settings can be seen even better in Figure 8.

Figure 8. Animated snapshots of effects of various settings previously described.